Subgroups — #17992780

Order 4736.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924442	C₂	1	1	yes	maximal, characteristic, complemented
2	#14557363	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#508	C₂	1	1	yes	maximal, characteristic
4	#11924472	—	2	1	no	—
5	#11924442	—	2	1	no	—
6	#135×C₃₇	—	2	1	no	—
7	Q₃₂×C₃₇	C₄	1	1	yes	characteristic
8	SD₃₂×C₃₇	—	2	1	no	—
9	D₁₆×C₃₇	C₄	1	1	yes	characteristic
10	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
11	#41×C₃₇	—	4	1	no	—
12	Q₁₆×C₃₇	—	2	1	no	—
13	SD₁₆×C₃₇	—	4	1	no	—
14	D₈×C₃₇	—	2	1	no	—
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	#10596934	—	4	1	no	—
17	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₃₇	D₄	1	1	yes	characteristic
19	Q₈×C₃₇	—	4	1	no	—
20	D₄×C₃₇	—	4	1	no	—
21	D₄×C₃₇	—	8	1	no	—
22	C₂×C₄×C₃₇	—	8	1	no	—
23	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
24	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
26	#64436	—	8	1	no	—
27	C₂²×C₃₇	—	8	1	no	—
28	C₂²×C₃₇	SD₃₂	1	1	yes	characteristic
29	C₄×C₃₇	—	8	1	no	—
30	C₄×C₃₇	#102	1	1	yes	characteristic
31	C₄×C₃₇	D₁₆	1	1	yes	characteristic
32	#1417	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	—	2	1	no	—
34	C₂×C₃₇	—	16	1	no	—
35	C₂×C₃₇	#357	1	1	yes	characteristic
36	#508	D₃₇	1	1	yes	characteristic
37	C₂×C₃₂	—	37	1	no	—
38	#368	—	37	1	no	—
39	C₃₇	#1417	1	1	yes	characteristic, complemented, Sylow
40	#135	—	2	1	no	—
41	Q₃₂	Dic₃₇	1	1	yes	characteristic
42	SD₃₂	—	2	1	no	—
43	D₁₆	Dic₃₇	1	1	yes	characteristic
44	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
45	#108	—	74	1	no	—
46	C₃₂	—	74	1	no	—
47	#41	—	4	1	no	—
48	Q₁₆	—	2	1	no	—
49	SD₁₆	—	4	1	no	—
50	D₈	—	2	1	no	—
51	M₁₆	—	148	1	no	—
52	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
53	C₁₆	C₂×Dic₃₇	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
55	Q₈	—	4	1	no	—
56	D₄	—	4	1	no	—
57	D₄	—	8	1	no	—
58	C₂×C₄	—	8	1	no	—
59	C₂×C₄	#10596939	1	1	yes	characteristic
60	C₈	—	296	1	no	—
61	C₈	#10596940	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₃₇	1	1	yes	characteristic
63	C₂²	—	8	1	no	—
64	C₂²	#11924480	1	1	yes	characteristic
65	C₄	—	8	1	no	—
66	C₄	#11924457	1	1	yes	characteristic
67	C₄	#11924477	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	16	1	no	—
70	C₂	#14557334	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924477
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting, prime radical	C₃₇×#508	C₂
socle	C₂×C₃₇	#357
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	#508	D₃₇
hypocenter	C₃₇	#1417
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#11924442	C₂	semidirect
2. #14557363	C₂	semidirect
39. C₃₇	#1417	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11924442	2
#14557363	2
C₃₇×#508	2
#1417	37